The study of low-dimensional semiconductor structures is one of the most intensively studied fields of modern semiconductor physics. Semiconductor structures in the nanometer range reveal a wealth of new and fascinating physical properties. Optical properties serve not only to characterize the semiconductor structures, but are themselves of fundamental physical interest. There are promising applications in optoelectronics and photonics and more can be expected. Describing the current state of research and recent developments, this work comprises a co-ordinated series of individual contributions from leading international authorities.